Are placement tests for incoming undergraduate mathematics students worth the expense of administration?

One of the tasks faced by undergraduate mathematics departments is placing incoming students into the appropriate mathematics classes for their abilities. This is often accomplished through giving a placement test at the time of student orientation. Dissatisfaction with the results of the placement test used at our university prompted us to write a new one. In this paper, we describe the writing of the new placement test and provide detailed results of a validity study on the test. Our results led us to conclude that placement testing does not work very well, and to suggest that undergraduate mathematics departments consider using existing data rather than give a separate placement test. In spite of this conclusion, we do decide to continue with our placement test, and we offer reasons for doing so.